Alternate Calculation of Eta Systematic

At the moment I am calculating the systematic error on A_LL from the presence of Etas in the signal reigon using theoretical predictions to estimate A_LL^eta.  The study below is an attempt to see how things would change if I instead calculated this systematic from the measured A_LL^eta.  Perhaps, also, this would be a good place to flesh out some of my original motivation for using theory predictions.

First order of buisness is getting A_LL^eta.  Since this was done in a quick and dirty fashion, I have simply taken all of my pion candidates from my pion analysis and moved my mass window from the nominal pion cuts to a new window for etas.  For the first three bins this window is .45 GeV/c² < mass < .65 GeV/c² and for the fourth bin this is .5 GeV/c² < mass < .7 GeV/c².  Here is a plot of A_LL^eta, I apologize for the poor labeling.

 

 I guess my first reason for not wanting to use this method is that, unlike the other forms of background, the Etas A_LL ought to be Pt dependent.  So I would need to calculate the systematic on a bin-by-bin basis, and now I start to get confused because the errors on these points are so large.  Should I use the nominal values?  Nominal values plus one sigma?  I'm not sure.

For this study I made the decison to use A_LL^true as the values, where A_LL^true is calculated from the above A_LL using the following formula:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

Remembering that a large portion the counts in the Eta mass window are from the combinatoric background.  I then calculate the background fraction or comtamination factor for this background (sorry I don't have a good plot for this) and get the following values

Bin   Bkg fraction

1      77.2%

2      60.9%

3      44.6%

4      32.6%

Plugging and chugging, I get the following values for A_LL^true:

Bin   A_LL^T

1      .0298

2      .0289

3      -.0081

4      .175

Using these values of ALL to calculate the systematic on A_LL^pion I get the following values:

Bin   Delta_A_LL^pion (x10^-3)

1      .33

2      .38

3      .63

4      3.1

Carl was right that these values would not be too significant compared to the quad. sum of the other systematics, except for final bin which becomes the dominant systematic.  In the end, I would not be opposed to using these values for my systematic *if* the people think that they tell a more consistent story or are easier to justify/explain than using the theory curves.  (i.e. if they represent a more accurate description of the systematic.)

Combinatoric Systematic

For the combinatoric background systematic we first estimate the background contribution (or contamination factor) to the signal reigon.  That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts.  The plots below show, for each of the four bins, the background fraction underneath the singal peak.  The background (simulation) is in green and the signal (data) is in black and the background that falls in the signal reigon is filled-in with green.

 

The background fractions for the bins are

Bin 1:  6.1%

Bin 2:  6.1%

Bin 3:  5.7%

Bin 4:  6.2%

 

Then I consider how much this background fraction could affect my measured asymmetry.  So I need to meausre the asymmetry in the high-mass reigon.  I do this, taking the mass window to be 1.2 to 2.0 GeV/c².  I do not expect this asymmetry to be Pt-dependant, so I fit the asymmetry with a flat line and take this to be the asymmetry of the background, regardless of Pt.  The plot below shows this asymmetry and fit.

 

Finally, I calculate the systematic error Delta_A_LL = A_LL^True - A_LL^Measured where:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

And C is the background fraction.  This yields in the end as a systematic error (x10^-3):

Bin 1:  1.0

Bin 2:  0.9

Bin 3:  1.6

Bin 4:  0.03

Eta Systematic

For the eta background systematic we first estimate the background contribution (or contamination factor) to the signal reigon.  That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts.  The plots below show, for each of the four bins, the background fraction underneath the singal peak.  The background (simulation) is in blue and the signal (data) is in black and the background that falls in the signal reigon is filled-in with.  Below that is the same four plots but blown up to show the contamination.

 

Here we blow up these plots

 

The background fractions for the bins are

Bin 1:  1.50%

Bin 2:  1.65%

Bin 3:  2.21%

Bin 4:  1.70%

 

Then I consider how much this background fraction could affect my measured asymmetry.  So I need to measure the asymmetry in the etas.  So instead of measuring the asymmetry in the etas I will use a theoretic prediction for A_LL.  From GRSV standard and GRSV min I approximate that the size of A_LL in my Pt range to be between 2 - 4%.

I stole this plot from C. Aidala's presentation at DNP in Fall 2007.  Since GRSV-Max is ruled out by the 2006 jet result I restrict myself only to min, standard and zero.  For a conservative estimate on the systematic, I should pick, for each Pt bin, the theory curve that maximizes the distance between the measured and theoretical asymmetries.  Unfortunately, at this time I do not have predictions for Pt above 8, so I must extrapolate from this plot to higher bins.  For the first two bins this maximum distance would correspond to GRSV standard (A_LL^bg ~ 0.02).  For the third bin, this would correspond to GRSV = 0 (A_LL^bg ~ 0.).  For the fourth bin (which has a negative measured asymmetry) I extrapolate GRSV standard to ~4% and use this as my background A_LL.

Systematic (x10^-3)

Bin 1:  0.18

Bin 2:  0.23

Bin 3:  0.43

Bin 4:  0.82

Low Mass Systematic

For the low mass background systematic we first estimate the background contribution (or contamination factor) to the signal reigon.  That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts.  The plots below show, for each of the four bins, the background fraction underneath the singal peak.  The background (simulation) is in red and the signal (data) is in black and the background that falls in the signal reigon is filled-in with red.

 

The background fractions for the bins are

Bin 1:  3.5%

Bin 2:  4.2%

Bin 3:  9.3%

Bin 4:  8.3%

 

Then I consider how much this background fraction could affect my measured asymmetry.  So I need to meausre the asymmetry in the low-mass reigon.  I do this, taking the mass window to be 0 to 0.7 GeV/c².  I do not expect this asymmetry to be Pt-dependant, so I fit the asymmetry with a flat line and take this to be the asymmetry of the background, regardless of Pt.  The plot below shows this asymmetry and fit.

 

Finally, I calculate the systematic error Delta_A_LL = A_LL^True - A_LL^Measured where:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

And C is the background fraction.  This yields in the end as a systematic error (x10^-3):

Bin 1:  1.0

Bin 2:  1.1

Bin 3:  3.7

Bin 4:  1.1